MEMS resonator structures offer an attractive alternative to quartz resonators as frequency references for many applications because of their lower cost and reduced form factor.
Temperature and process variations impact the oscillation frequency of Silicon MEMS resonators beyond the tolerance limits of many applications. MEMS resonators are for example used in reference oscillators in RF receiver circuits. The resonance frequency of a MEMS resonator in silicon exhibits a temperature drift of typically −30 ppm/K. For some applications this drift needs to be reduced significantly. For example, when using a MEMS resonator in a GSM reference oscillator the drift needs to be below +/−20 ppm or even +/−10 ppm over a temperature range of 100K.
The main cause of the temperature dependence of the resonance frequency is the negative temperature coefficient of the elastic modulus exhibited by all but a few materials. This results in a reduced spring constant at higher temperatures, and hence a reduced frequency.
Several solutions have been proposed to correct for the temperature dependence:
Active temperature compensation techniques involve keeping the resonator at a constant temperature by placing the resonator in a temperature controlled feedback loop. In this case, the temperature is measured on, or in close vicinity of the resonator. This temperature is then stabilized by heating the resonator to a preset temperature. This approach is limited by the accuracy of the temperature measurement used to determine the required correction factor.
Passive temperature compensation techniques involve designing the resonator to reduce the dependency of the frequency on temperature. One approach is to combine mono-crystalline silicon with amorphous SiO2, since the Young's modulus of SiO2 exhibits an opposite temperature dependency to that of silicon. More generally, this approach involves deposition/growth of layers with positive temperature coefficient of the elastic modulus to reduce the resulting error, but these approaches are sensitive to small variations in the thickness of the deposited layer.
There is therefore a need for a simple and easily detectable technique that eliminates sensitivity to all non-local process variations and determines the correction factor due to temperature changes to very high accuracy.